Category Using gret l for Principles of Econometrics, 4th Edition


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Simultaneous Equations Models

In Chapter 11 of POE4 the authors present a model of supply and demand. The econometric model contains two equations and two dependent variables. The distinguishing factor for models of this type is that the values of two (or more) of the variables are jointly determined. This means that a change in one of the variables causes the other to change and vice versa. The estimation of a simultaneous equations model is demonstrated using the truffle example which is explained below.

11.1 Truffle Example

Consider a supply and demand model for truffles:

qi =ai + a2pi + a3psi + a^dii + ed (11.1)

qi =ві + в Pi + вз pfi + es (11.2)

The first equation (11.1) is demand and q us the quantity of truffles traded in a particular French market, p is the market price of truffles, ps is the market price ...

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Seemingly Unrelated Regressions

The acronym SUR stands for seemingly unrelated regression equations. SUR is another way of estimating panel data models that are long (large T), but not wide (small N). More generally though, it is used to estimate systems of equations that do not necessarily have any parameters in common and whose regression functions do not appear to be related. In the SUR framework, each firm in your sample is parametrically different; each firm has its own regression function, i. e., different intercept and slopes. Firms are not totally unrelated, however. In this model the firms are linked by what is not included in the regression rather than by what is. The firms are thus related by unobserved factors and SUR requires us to specify how these omitted factors are linked in the system’s error structure...

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Error Correction

Cointegration is a relationship between two nonstationary, I(1), variables. These variables share a common trend and tend to move together in the long-run. In this section, a dynamic relationship between I(0) variables that embeds a cointegrating relationship known as the short-run error correction model is examined.

Start with an ARDL(1,1)

yt = S + dryt-i + 5oXt + Sixt-i + vt (12.7)

after some manipulation (see POE4 for details)

Ayt = -(1 – di)(yt-i – ві – foxt-1) + SoAxt + SiAxt-i + vt (12.8)

The term in the second set of parentheses is a cointegrating relationship. The levels of y and x are linearly related. Let a = (1 — 91) and the equation’s parameters can be estimated by nonlinear least squares.

In gretl this is easiest done in a script. There are basically three steps...

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Selection Bias

Selection bias occurs when your sample is truncated and the cause of that truncation is corre­lated with your dependent variable. Ignoring the correlation, the model could be estimated using least squares or truncated least squares. In either case, obtaining consistent estimates of the re­gression parameters is not possible. In this section the basic features of the this model will be presented.

Consider a model consisting of two equations. The first is the selection equation, defined

z* = Yi + Y2Wi + Ui, i = 1,… ,N

where z* is a latent variable, Yi and y2 are parameters, wi is an explanatory variable, and ui is a random disturbance. A latent variable is unobservable, but we do observe the dichotomous variable

The second equation, called the regression equation, is the linear model of in...

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